Nepela, who competed for Czechoslovakia, was the first Slovak Olympic champion. He was coached by Hilda Mudra. After his death due to AIDS-related complications, his native city of Bratislava in the Slovak Republic named the Winter Stadium, Nepela's home base as a member of Slovan, after him, and continues to hold a prestigious annual ISU international skating competition called the Ondrej Nepela Memorial.

In his autobiography When Hell Freezes Over, Should I Bring My Skates?, Toller Cranston describes (p. 54) a brief tryst with Nepela, and remembers him this way:

"Many people perceived him as handsome or even as beautiful. He evidenced an androgynous, Nijinsky-like quality. In physical features he reminded me of a Tartar from the Eastern European steppes, with slanted Mongolian eyes yet light skin. He was small. He was fine. He was a steady, nerveless competitor, completely lacking in personality or finesse: a generic Soviet-satellite skater who had been browbeaten into becoming a fine technician - less fine in free skating and more precise or womanlike in the school figures."

A worthy successor to Karol Divin, with whom he represented Czechoslovakia at his first Olympics in Innsbruck in 1964, he was assisted in his achievement by the legendary trainer, "auntie" Hilda Mudra. He bid farewell to the world of amateur sport with a freestyle mark of 6.0 for artistic impression at the World Championships in 1973.

In 1997, the Slovak Rerpublic emitted a mail stamp in his honour. In December 2000, the Slovak Republic named him Slovakian athlete of the century; Mudra received the award on his behalf.